Uncertainties in LMI systems

[Stanislav Tomashevich]

Hello Johan!

I have some problems with solving LMI systems with uncertainties. I will be thank if you can help me or give right way!

My LMI systems is

\begin{cases}
A*P+P*A'-a*(B*T+T'*B')+2*er*P<0
A*P+P*A'-a*(B*T+T'*B')+2*el*P>0
\end{cases}

A, B -- given matrixes, P, T -- variables, er and el -- given scalars -- bounds of LMI region. Uncertain is 'a' and I want next case: 0<a<=2. But I'm trying to make more simple at first:  0.1<=a<=2 and have problems with result: taking a from 0.1<=a<=2 and substituting in equations it isnt fits LMI region. I use SeDuMi, SDPT3 solvers.

Where is problem in my case and what should I do to have correct result?

Thanks in advance and
Best regards

[Johan Löfberg]

Not sure what you are asking. Are you wondering about the robust optimization framework in YALMIP? Then you should be able to write it exactly like that, and the model YALMIP will derive is

A*P+P*A'-.1*(B*T+T'*B')+2*er*P<0
A*P+P*A'-.1*(B*T+T'*B')+2*el*P>0
A*P+P*A'-2*(B*T+T'*B')+2*el*P>0
A*P+P*A'-.1*(B*T+T'*B')+2*el*P>0

Strict inequalities are not allowed, so you have to fix your code accordingly